LAPLACE. 165 



disposal will be employed in readiug your beautiful work.'' It would 

 appear that the words, •' the first six months,''^ deprive the i)hrase of the 

 character of a common-place expression of thanks, and convey a just 

 appreciation of the importance and difficulty of the subject-matter. 



On the 5th Frimaire, in the year XI, the reading of some chapters of 

 the volume which Laplace had dedicated to him was to the general " a 

 new occasion for regretting that the force of circumstances had directed 

 him into a career which removed him from the pursuit of science." 



" At all events," added he, " I have a strong desire that future gen- 

 erations, upon reading the Mecaniqiie Celeste, shall not forget the es- 

 teem and friendship which I have entertained toward its author." 



On tho 17th Prairial, in the year XIII, the general, uow become Em- 

 peror, wrote from Milan : " The Mecanique Celeste appears tO me des- 

 tined to shed new luster on the age in which we live." 



Finally, on the 12th of August, 1812, Xapoleon, who had jutt received 

 the Traite du Calcul des Probabilites wrote from Witepask the letter 

 which we transcribe textually : 



"There w'as a time when I would have read with interest your Traite 

 du Calcul des Prohahilites. For the present, I must confine myself to 

 expressing to you the satisfaction which I experience every time that I 

 see you give to the world new works which serve to improve and ex- 

 tend the most important of the sciences and contribute to the glory 

 of the nation. The advancement and the improvement of mathemati- 

 ical science are connected with the prosperity of the state." 



I have uow arrived at the conclusion of the task which I had im- 

 posed upon myself. I shall be pardoned for having given so detailed 

 an exposition of the principal discoveries for which philosophy, astron- 

 omj', and navigation are indebted to our geometers. 



It has apxjeared to me that in thus tracing the glorious past, I have 

 shown our contemporaries the full extent of their duty towards the 

 country. In fact, it is for nations especially to bear in remembrance 

 the ancient adage, noblesse oblige. 



Appendix A. 



The following is a brief notice of some other interesting results of the 

 i-esearches of Laplace which have not been mentioned in the text : 



Method for determining the orbits of comets. — Since comets are gen- 

 erally visible only during a few days or weeks at the utmost, the 

 determination of their orbits is attended with peculiar difficulties. 

 The method devised by Newton for effecting this object was in every 

 respect worthy of his genius. Its practical value was illustrated by the 

 brilliant researches of Halley on cometary orbits. It necessitated, how- 

 ever, a long train of tedious calculations, and, in consequence, was not 

 much used, astronomers generally preferring to attain the same end by 

 a tentative process. In the year 1780, Laplace communicated to the 



